Wenliang Zhang

Email: wlzhang at uic.edu

Address: UIC MSCS Department (M/C 249)

851 S. Morgan St.

Chicago, IL 60607-7045

Papers (published or accepted):

23. Poincare duality in modular coinvariant rings (with M. Sezer)

Proc. Amer. Math. Soc., to appear.

22. F-pure thresholds of homogeneous polynomials (with D. Hernandez, L. Nunez Betancourt, and E. Witt)

Michigan Math. Journal, to appear.

21. Frobenius splitting in commutative algebra (with K. Smith)

MSRI volume, 65 (2016), no.1, 57–87.

20. A survey on Lyubeznik numbers (with L. Nunez Betancourt and E. Witt)

Contemp. Math. 657, 137--163.

19. An extension of a theorem of Hartshorne (with M. Katzman and G. Lyubeznik)

Proc. Amer. Math. Soc. 144 (2016), no. 3, 955--962.

18. Eulerian Graded D-modules (with L. Ma)

Math. Res. Lett. 21 (2014), no. 1, 149–167.

17. Local cohomology modules of a smooth Z-algebra have finitely many associated primes (with B. Bhatt, M. Blickle, G. Lyubeznik, and A. Singh)

Invent. Math. 197 (2014), no. 3, 509–519.

16. Rings of Frobenius operators (with M. Katzman, K. Schwede, and A. Singh)

Math. Proc. Cambridge Philos. Soc. 157 (2014), no. 1, 151–167.

15. Annihilators of Artinian modules compatible with a Frobenius map (with M. Katzman)

J. Symbolic Comput. 60 (2014), 29–46.

14. Castelnuovo-Mumford regularity and the discreteness of F-jumping coefficients in graded rings (with M. Katzman)

Trans. Amer. Math. Soc. 366 (2014), no. 7, 3519–3533.

13. Cartier modules on toric varieties (with J.-C. Hsiao, and K. Schwede)

Trans. Amer. Math. Soc. 366 (2014), no. 4, 177–1795.

12. Bertini theorems for F-singularities (with K. Schwede)

Proc. London Math. Soc., (3) 107 (2013), no. 4, 851–874.

11. Estimates for F-jumping numbers and bounds for Hartshorne-Speiser-Lyubeznik numbers (with M. Mustata)

Nagoya Math. J. 210 (2013), 133--160.

10. Test ideals via a single alteration and discreteness and rationality of F-jumping numbers (with K. Schwede and K. Tucker)

Math. Res. Letters, 19 (2012), no. 1, 191–197.D-Modules in Commutative Algebra

9. Two interesting examples of D-modules in characteristic p > 0 (with M. Katzman and G. Lyubeznik)

Bulletin of London Math. Soc., (2012) 44(6): 1116–1122

8. A property of the Frobenius map on a polynomial ring (with G. Lyubeznik and Y. Zhang)

Contemp. Math. 555 (Proceedings of PASI 2009), 137–144.

7. An upper bound on the number of F-jumping coefficients of a principal ideal (with M. Katzman and G. Lyubeznik)

Proc. Amer. Math. Soc. 139 (2011), 4193–4197.

6. Lyubeznik numbers of projective schemes

Adv. Math. 228 (2011), 575–616.

5. Discreteness and rationality of F-jumping numbers on singular varieties (with M. Blickle, K. Schwede, and S. Takagi)

Math. Ann. 347 (2010), no. 4, 917–949.

4. On Frobenius powers and colon ideals,

Comm. Alg. 37 (2009), no.7, 2391–2395.

3. On the localization theorem for F-pure rings (with K. Shimomoto)

Journal of Pure and Applied Algebra, (2009), no. 6, 1133–1139.

2. On the discreteness and rationality of F-jumping coefficients (with M. Katzman and G. Lyubeznik)

Journal of Algebra, 322 (2009), no. 9, 3238–3247.

1. On the highest Lyubeznik number of a local ring

Compositio Mathematica, 143 (2007), no. 1, 82–88.

Preprints (submitted or in preparation):

1. F-singularities in families (with Z. Patakfalvi, and K. Schwede)

arXiv:1305.1646, submitted in 2013.

2. The support of local cohomology modules (with M. Katzman)

arXiv:1509:01519, submitted in 2015.

3. A note on growth of regularity with respect to Frobenius

arXiv:1512:00049, submitted in 2015.

4. On injective dimension of F-finite F-modules and holonomic D-modules

arXiv:1606.00536, submitted in 2016.

5. Stabilization of cohomology of thickenings (with B. Bhatt, M. Blickle, G. Lyubeznik, and A. Singh)

arXiv:1605.09492, submitted in 2016.

6. F-singularities under generic linkage (with L. Ma, J. Page, R. Rebhuhn-Glanz, and W. Taylor)

arXiv:1607.03972, submitted in 2016.

7. Global parameter test ideals (with M. Katzman, S. Murru, and J. Velez)

arXiv:1607.01947, submitted in 2016.

8. Content of local cohomology, parameter ideals, and robust algebras (with M. Hochster)

in preparation.

9. D-module length of local cohomology modules (with M. Katzman, L. Ma, and I. Smirnov)

in preparation.

Teaching:

Spring 2016: Math 310 (Linear Algebra)

Fall 2015: Math 330 (Abstract Algebra)

REU: Chris Skalit, Kevin Tucker and myself are organizing an REU program in Commutative Algebra in Summer 2016. More information can be found here.

Lecture notes:

1. Local cohomology workshop at UIC, 02/27--03/01, 2015. (Notes)

2. Introduction to modular curves and modular forms, Fall 2014. (Notes)

Past Events Organized:

- D-Modules in Commutative Algebra, (08/10--08/14, 2015), CIMAT, Guanajuato, Mexico.
- Mathematical Research Community in Commutative algebra, (06/07--06/13, 2015), Snowbird, UT.
- Local cohomology workshop, (02/27--03/01, 2015), Chicago, IL.
- Focus period on Local cohomology and Regularity, (04/01--04/26, 2013), Special Year in Commutative Algebra at MSRI.
- Computational workshop on Frobenius singularities and invariants, (05/29--06/01, 2012), Ann Arbor, MI.